The interaction of methylene blue (MB) dye with natural coal (collected from coal landfills of the Kosovo Energy Corporation) in aqueous solutions was studied using adsorption, kinetics, and thermodynamic data, and Monte Carlo (MC) calculations. In a batch procedure, the effects of contact duration, initial MB concentration, pH, and solution temperature on the adsorption process were examined. The Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich (D–R) isotherms were used to examine the equilibrium adsorption data. The equilibrium data fit well to the Freundlich and Langmuir adsorption isotherm models; however, the Freundlich model suited the adsorption data to a slightly better extent than the Langmuir model. The kinetics experimental data was fitted using pseudo-first-order, first-order, pseudo-second-order, second-order, Elvoich equation, and diffusion models. The pseudo-second-order rate model manifested a superlative fit to the experimental data, while the adsorption of MB onto coal is regulated by both liquid film and intraparticle diffusions at the same time. Thermodynamic parameters, such as Gibbs free energy (ΔG⁰), enthalpy (ΔH⁰), and entropy (ΔS⁰) were calculated. The adsorption of MB was confirmed to be spontaneous and endothermic. The theoretical results were in agreement with the experimental ones.

Methyl Violet (MV) was removed from aqueous solutions by adsorption onto halloysite nanoclay (HNC) employing equilibrium, kinetics, thermodynamic data, molecular modellingR (MD), and Monte Carlo (MC) simulations. The chosen experimental variables were pH, temperature, starting MV concentration, contact time, and adsorbent dosage. The adsorption rate was determined to increase with increasing contact time, initial dye concentration, pH, and temperature. The Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich (D-R) isotherms were utilized to determine the adsorption capacity of HNC. The Langmuir equation matched equilibrium data better than the other models, whereas the pseudo-second-order model better described kinetic data, and thermodynamic analyses revealed that the adsorption process was spontaneous, endothermic, and physisorption-based. This study focused on two distinct molecular mechanics-based theoretical approaches (MC and MD). These techniques enabled a molecular comprehension of the interaction between the MV molecule and the halloysite surface. Theoretical results were consistent with experimental findings. The outcomes revealed that HNC is an excellent dye adsorbent for industrial effluents.

To better understand graphene and its interactions with polycyclic aromatic hydrocarbons (PAHs), density-functional-theory (DFT) computations were used. Adsorption energy is likely to rise with the number of aromatic rings in the adsorbates. The DFT results revealed that the distance between the PAH molecules adsorbed onto the G ranged between 2.47 and 3.98 Å depending on the structure of PAH molecule. The Non-Covalent Interactions (NCI) plot supports the concept that van der Waals interactions were involved in PAH adsorption onto the Graphene (G) structure. Based on the DFT-calculated adsorption energy data, a rapid and reliable method employing an empirical model of a quantitative structure–activity relationship (QSAR) was created and validated for estimating the adsorption energies of PAH molecules onto graphene.

Water pollution from phenols remains a critical concern due to their persistence, toxicity, and industrial prevalence. Graphene oxide (GOx), with its functional groups and large surface area, offers strong adsorption potential. Using density functional theory (DFT), reduced density gradient (RDG), and quantitative structure–activity relationship (QSAR), we examined how protonation and substituents influence phenol adsorption. Deprotonated phenolates bind more strongly to GO than neutral species via electrostatics and H-bonding. Substituents alter affinity: halogens enhance it, bulky alkyls hinder it, and nitro groups show electron-withdrawing effects. Bisphenolate A displayed multidentate binding. QSAR models reproduced DFT energies with R² > 0.99, enabling fast prediction. These results highlight how pH speciation and substituents govern adsorption on GO, guiding the design of efficient water treatment materials.